This paper introduces a graduate course, continuum mechanics, which is designed for and taught to graduate students in a Mechanical Engineering (ME) program. The significance of continuum mechanics in engineering education is demonstrated and the course structure is described. Methods used in teaching this course such as topics, class organization, and evaluation instruments are explained. Based on the student learning outcomes and feedbacks, the course objectives were achieved. This paper shows that ME program objectives are well supported by this course. (Contains 1 figure and 1 table.)